TABLE OF CONTENTS

Mathops is committed to helping Michigan students achieve. Most text books do not cover Michigan’s curriculum standards. The Mathops Michigan Supplementary Curriculum is designed to meet the needs of Michigan 8th grade and Algebra students.

**Supplementary** 8th Grade links are in gold. **
Supplementary** Algebra one links are
in green.

Notice: Some 8th grade lessons are also part of the algebra curriculum. Please check the standards links under each section title for standards information.

- Adding Integers Using a Number Line
- Football and Other Integer Word Problems
- Subtracting Integers Using a Number Line
- Introduction to Absolute Value
- Using Absolute Value to Combine Integers
- Multiplying Integers Using a Number Line
- Multiplying Integers- Rules and Tricks
- Dividing Integers
- Dividing Integers- Rules and Tricks

- Factoring Integers
- Least Common Multiple
- Simplifying Fractions
- Adding and Subtracting Fractions
- Multiplying Fractions
- Dividing Fractions
- Converting Fractions to Decimals

- Zero, Identity and Inverse Properties
- Commutative and Associative Properties and Mental Math
- Distributive Property and Mental Math
- Properties Cheat Sheet

- Like Terms
- Expressions vs. Equations
- Solving One Step Equations Using Addition and Subtraction
- Solving One Step Equations Using Multiplication and Division
- Solving Two Step Equations
- Multi Step Equations - Combining Like Terms & Variables on Both Sides
- Multi Step Equations with Parenthesis
- Combining Like Terms with Multiple Variables

- Weighted Averages Introduction: Slugging Average
- Weighted Averages: Weighted Grades
- Weighted Averages Grade Point Average Example
- Weighted Averages: Methods of Solving and Figuring in Midterm and Final Exam Grades
- Weighted Averages Social Studies Connection

- Relations and Functions Defined
- Function Notation
- Parent Functions
- Introduction to Graphing Transformations

- Introduction to Linear Functions
- Linear Tables from Graphs
- Slope From Two Points
- Slope - Counting Rise over Run on a Graph
- Writing a Slope-Intercept Equation from a Graph
- Graphing Slope-Intercept Equations
- Creating a table from an Equation
- Graphing a Slope-Intercept Equation Using Intercepts
- Writing a Slope-Intercept Equation from the Slope and One Point
- Writing a Slope-Intercept Equation from Two Points
- Constant Functions
- Parallel Lines
- Perpendicular Lines
- Standard Form - Graphing Using X and Y Intercepts
- Converting From Standard Form to Slope-Intercept Form
- Writing the Point Slope Form of a Line Given the Slope and One Point
- Graphing Linear Equations in Point Slope Form
- Converting From Point Slope to Slope Intercept Form
- Piecewise Functions
- Linear Graphs: Transformations

- Creating Scatter Plots
- Scatter Plots and Correlation
- Least Squares Method of Determining Line of Best Fit
- Linear Correlation and Pearson's Correlation Coefficient
- Clusters and Outliers
- Scatter Plot Tools - Using MS Excel

- Solving Systems of Linear Equations By Graphing
- Solving Systems of Equations using Simple Substitution Part One
- Solving Systems of Equations using Simple Substitution Part Two
- Solving Systems using Substitution and the Distributive Property
- Solving Systems using Substitution and the Distributive Property (including reformatting equations)
- Solving Systems using Elimination
- Solving Systems using Elimination (including reformatting equations)
- Solving Systems Using Elimination (finding the least common multiple)
- Systems with no solutions and infinitely many solutions (parallel and coincide)
- Systems with Three equations and Three Variables

- That Nasty Two Faced Symbol - Which is Which?
- Graphing Inequalities with One Variable
- Solving and Graphing Positive One Step Inequalities
- Solving and Graphing Negative One Step Inequalities
- Solving and Graphing Two Step Inequalities
- Solving Multi Step Inequalities
- Graphs of Compound Inequalities
- Solving Compound Inequalities
- Solving Compound Inequalities with Negative Coefficients
- Graphing Inequalities with Two Variables (solid vs. dashed)
- Graphing Two Variable Inequalities in Standard Form
- Graphing Two Variable Inequalities in Point-Slope Form
- Graphing Systems of Linear Inequalities

- Properties of Exponents
- Product Property - Multiplying Polynomials
- Power of a Power Property
- Power of a Product Property
- Combining the Multiplication Properties
- Power of a Fraction Property
- Quotient Property of Exponents (positive exponents)
- Zero and Negative Exponents
- Quotient Property of Exponents (positive and negative)
- Arithmetic and Geometric Sequences
- Recursive Linear Functions
- Exponential Recursive Functions
- Equations to Model Exponential Recursive Calculations

- Introduction to Polynomials - degree of polynomials
- Adding and Subtracting Polynomial Functions
- Adding and Subtracting Polynomial Functions With Function Notation
- Multiplying Binomials
- Multiplying Polynomials
- Multiplying with Function Notation
- Dividing Polynomials - Simplifying
- Dividing with Function Notation

- Simplifying Square Roots
- Simplifying Square Roots Containing Variables
- Simplifying Square Root Expressions Using the Complex Conjugate

- Introduction to Quadratic Equations
- Graphs and Solutions of Functions in the Form of ax² and ax² + c
- Area Models of Equations in the Form ax² + bx
- Area Models of Equations in the Form ax² + bx + c
- Converting from Factored Form to Standard Form
- Factoring Equations in ax² + bx format
- Factoring Equations in ax² + bx + c format with a = 1
- Factoring Equations in ax² + bx + c format with a Not = 1 using Guess and Check
- Special Factors - Difference of Two Squares
- Factoring 4 Terms by Grouping
- Using Grouping Strategies with Trinomials
- Getting to the Root of it All - Finding the Roots and Solutions by Factoring
- Using Roots to Find the Axis of Symmetry
- Using the Axis of Symmetry to Find the Vertex Point
- Graphing Using FRAV
- The -b Over 2a Shortcut
- Writing the Vertex form of a Quadratic Equation
- Stating the Vertex from the Vertex Form
- Converting from Vertex form to Standard Form
- Solving Equations by Taking the Root (ax² + bx)
- Solving Vertex Form Equations by Taking the Root
- Solving Equations by Completing the Square
- What is the Quadratic Formula
- Using the Quadratic Formula
- Imaginary Numbers
- Complex Numbers
- More Recursive Functions

- Power/Polynomial Functions: Equations
- Power/Polynomial Functions: Tables
- Introduction to the Symmetry of Power/Polynomial Functions
- Solving Power/Polynomial Functions by Taking the Root
- Factoring Power/Polynomial Functions and Expressions Using GCF
- Solving Power/Polynomial Functions Using GCF
- Factoring Power/Polynomial Functions and Expressions Using Grouping
- Solving Power/Polynomial Functions Using Grouping
- Factoring Power/Polynomial Functions Using Special Products
- Solving Power/Polynomial Functions Using Special Products
- Factoring Power/Polynomial Functions – Choosing the Best Method
- Graphs of Power/Polynomial Functions
- Graphs: Transformations to Power/Polynomial Function Output
- Graphs: Transformations to Power/Polynomial Function Input

- Introduction to Radicals and Radical Functions Including Rational Exponents
- Properties of Radicals
- Simplifying Radical Expressions
- Rationalizing Radical Denominators
- Adding and Subtracting Radicals
- Multiplying and Dividing Radicals
- Properties of Rational Exponents
- Simplifying Rational Exponents
- Adding and Subtracting with Rational Exponents
- Multiplying and Dividing with Rational Exponents
- Solving Radical Equations and Equations with Rational Exponents
- Radical Functions with Extraneous Solutions
- Translations to Graphs of Square Root Functions - Domain and Range
- Translations to Graphs of Cube Root Functions

- Direct Variation
- Inverse Variation
- Solving Variation Using Proportions
- Nth Power Variation
- Joint Variation (Advanced Topic)

- Introduction to Rational Functions
- Simplifying Rational Functions
- Solving Rational Functions
- Holes, Asymptotes, and Graphs
- Horizontal Asymptotes

- Composite Functions
- Introduction to Inverse Functions
- Writing Inverse Functions
- Graphs of Inverse functions
- The Horizontal Line Test
- Verifying Inverse Relations
- Piecewise Combined